Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 337: 33

$1$

We can rewrite the expression as two terms $sec^2\theta + 1$ in the integrand, which is much simpler to integrate. Recall the formula $$\frac{d}{dx} tan \theta = sec^2\theta $$ As such, we get the integral $tan\theta + \theta$ We now substitute our bounds $\frac{\pi}{4} $and $0$ to get $(1 + 0) - (0 + 0) = 1$